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AMS 518, Advanced Stochastic Models, Risk Assessment, and Portfolio Optimization

The course provides a thorough treatment of advance risk measurement and portfolio optimization, extending the traditional approaches to these topics by combining distributional models with risk or performance measures into one framework. It focuses on, among others, the fundamentals of probability metrics and optimization, new approaches to portfolio optimization and a variety of essential risk measures. Numerical exercises and projects in a high-level programming environment will be assigned.

Prerequisite: AMS 512 or AMS 516 or AMS 522

Fall, 3 credits, ABCF grading



Course Materials  (recommended):
Zabarankin, M. and S. Uryasev. “Statistical Decision Problems. Selected Concepts and Portfolio Safeguard Case Studies.” Optimization and Its Applications, Vol. 85, Springer, 2014; ISBN:  978-1-4939-5325-7 (paperback)



Learning Outcomes:

1) Understand the concepts of probability and optimization
      * Continuous probability distributions and probabilistic inequalities;
      * Unconstrained/constrained optimization.

2) Understand the definitions of risk and uncertainty
      * Value-at-risk;
      * Average VaR;
      * Backtesting risk measures.

3) Demonstrate skills in building portfolio allocation
      * Mean-variance optimization problems, and mean-risk problems;
      * Reward-to-Risk ratios.

4) Understand the method of adaptive data cleaning and basic stylized facts.

5) Understand the model of seasonal volatility and realized volatility dynamics.

6) Demonstrate skill with forecasting risk and return and correlation/multivariate risk.

7) Understand the trading models and theory of heterogeneous markets.